This is probably relatively trivial (at least from my not-actually-a-Muslim perspective, so I do apologize if it actually isn't trivial), but it's a question that's gotten stuck in my mind anyway: if one were physically present within the walls of the Kaaba, would there be a specific direction that one be obligated to face during salat?
Thank you for taking the time to answer.
While you are inside the Kaa'bah then you can pray in any direction. Everywhere you will turn your face, you will find the direction of Qiblah. If you are praying behind an Imam inside the Kaab'ah who is also present inside the Kaa'bah then you should not be standing in front of the Imam. Otherwise, your Salah will become invalid because you went ahead of your Imam.
And Allah knows best.
Mufti Ikram ul Haq
Fatwa Center of America